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On Possible Values of Upper and Lower Derivatives with Respect to Convex Differential Bases

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Abstract

It is proved that if a convex density-like differential basis B is centered and invariant with respect to translations and homotheties, then the integral means of a nonnegative integrable function with respect to B can boundedly diverge only on a set of measure zero (this generalizes a theorem of Guzmán and Menarguez); it is established that both translation and homothety invariances are necessary.

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  1. A. Tseretaeli Kutaisi State University, Russia

    G. G. Oniani

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  1. G. G. Oniani
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Oniani, G.G. On Possible Values of Upper and Lower Derivatives with Respect to Convex Differential Bases. Mathematical Notes 76, 711–722 (2004). https://doi.org/10.1023/B:MATN.0000049670.36842.71

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  • DOI: https://doi.org/10.1023/B:MATN.0000049670.36842.71

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